Question

If A+B= 45° then prove that: tanA+ tanB+ tanA. tanB​

Answer 1

See Explanation

Explanation:

`A+B= 45 \degree \\ \\ assuming \: \tan \: on \: both \: sides \\ \\\implies \: \tan( A+B)= \tan 45 \degree \\ \\ \implies \: \tan( A+B)= 1 \: \: \\ ( \because \: \tan 45 \degree = 1) \\ \\ \implies \: (\tan \: A +\tan \: B )/(1 - \tan \: A .\tan \: B ) = 1 \\ \\ \implies \: \tan \: A +\tan \: B = 1 - \tan \: A .\tan \: B \\ \\ \purple{ \implies }\: \orange{ \bold{\tan \: A +\tan \: B + \tan \: A .\tan \: B= 1 }} \\ \\ thus \: proved`